is the case for iphone 15 also suitable with iphone 13

No.

Maybe.

The regular iPhone 15 and iPhone 13 are essentially the same size and shape so its possible some cases for the iPhone 15 would work with an iPhone 13. But its going to come down to actually testing the case to see if it actually works.

The Pro and Pro Max versions have different dimensions and larger camera bumps on the 15 so the cases may not work though for the 13 Pro or Pro Max phones.